Theorem 2rexbii 1670

Description: Inference adding 2 restricted existential quantifiers to both sides of an equivalence.

Hypothesis

Ref	Expression
ralbii.1	|- (ph <-> ps)

Assertion

Ref	Expression
2rexbii	|- (E.x e. A E.y e. B ph <-> E.x e. A E.y e. B ps)

Proof of Theorem 2rexbii

Step	Hyp	Ref	Expression
1		ralbii.1	. . 3 |- (ph <-> ps)
2	1	rexbii 1668	. 2 |- (E.y e. B ph <-> E.y e. B ps)
3	2	rexbii 1668	1 |- (E.x e. A E.y e. B ph <-> E.x e. A E.y e. B ps)

Syntax hints:   <-> wb 146  E.wrex 1646

This theorem is referenced by:  unxpdomlem 4843  dffsum 6998

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-rex 1650

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